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Paha777 [63]
2 years ago
8

A man starts walking from home and walks 3 miles at north of west, then 5 miles at west of south, then 4 miles at north of east.

If he walked straight home, how far would he have to the walk, and in what direction
Mathematics
1 answer:
Annette [7]2 years ago
8 0

Answer:

Step-by-step explanation:

We shall find the solution of this problem with the help of vector notation of i , j , which show east and  north direction .

The first displacement can be represented by the following

D₁ = - 3 cos 45 i + 3 sin45 j = - 3 / √2 i + 3 / √2 j

The second  displacement can be represented by the following

D₂ = - 5 cos 45 i - 5 sin45 j = - 5 /√2 i - 5 /√2 j

The third  displacement can be represented by the following

D₃ =  4 cos 45 i + 4 sin45 j =  4 /√2 i + 4 /√2 j

Total displacement D =

D₁ +D₂ + D₃

= i ( -3 -5 + 4 ) / √2 + j ( 3 - 5 + 4 ) / √2 j

= - 4  / √2 i + 2 / √2 j

D = - 2.8288 i + 1.414 j

Magnitude of D

= √ ( 2.8288² + 1.414² )

= 3.16 miles

For direction we calculate angle with X axis

Tanθ = 1.414 / 2.8288

θ = 26 °

As x is negative and Y is positive ,

the direction will be north of west .

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Answer:

7 or 8 miles per hour

Step-by-step explanation:

3 0
3 years ago
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Ming took a cab across town. His fare was \$22$22, and he leaves an 18\%18% tip. What is the total amount Ming pays the cab driv
Lilit [14]

Answer:

$25.96

Step-by-step explanation:

First, you turn the percent into a decimal, which gives you .18.  Then, you multiply $22 by .18.  Finally, you add the $3.96 that you get by multiplying $22 by .18, and you get the answer that is above.  Plz mark brainliest if correct.

6 0
3 years ago
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(7a^3 -2a-2)+(-5a+3)
atroni [7]

Answer:

7a  3  −7a+1

Step-by-step explanation: I hope this help.

STEP

1

:

Equation at the end of step 1

 ((7a3 -  2a) -  2) +  (3 - 5a)

STEP

2

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Polynomial Roots Calculator :

2.1    Find roots (zeroes) of :       F(a) = 7a3-7a+1

Polynomial Roots Calculator is a set of methods aimed at finding values of  a  for which   F(a)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  a  which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q   then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient

In this case, the Leading Coefficient is  7  and the Trailing Constant is  1.

The factor(s) are:

of the Leading Coefficient :  1,7

of the Trailing Constant :  1

Let us test ....

  P    Q    P/Q    F(P/Q)     Divisor

     -1       1        -1.00        1.00      

     -1       7        -0.14        1.98      

     1       1        1.00        1.00      

     1       7        0.14        0.02      

Polynomial Roots Calculator found no rational roots

Final result :

 7a3 - 7a + 1

6 0
2 years ago
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then divide by nine to get

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I a failin really need help
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